## Turing

December 24, 2013

Barry Cooper‘s email to the ATY/TCAC email list (Dated Tue, 24 Dec 2013 00:08:33 +0000 (GMT)):

Just a quick update to give details of the Royal Pardon for Alan Turing – here is an official release, embargoed until 00:01 this morning:

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PARDON FOR WW2 CODE-BREAKER TURING
By Jamie Grierson, Press Association Home Affairs Correspondent

Second World War code-breaker Alan Turing has been given a posthumous royal pardon for a 61-year-old conviction for homosexual activity. Dr Turing, who was pivotal in breaking the Enigma code, arguably shortening the Second World War by at least two years, was chemically castrated following his conviction in 1952.

His conviction for “gross indecency” led to the removal of his security clearance and meant he was no longer able to work for Government Communications Headquarters (GCHQ) where he had continued to work following service at Bletchley Park during the war.

Dr Turing, who died aged 41 in 1954 and is often described as the father of modern computing, has been granted a pardon under the Royal Prerogative of Mercy by the Queen following a request from Justice Secretary Chris Grayling. “Dr Alan Turing was an exceptional man with a brilliant mind,” Mr Grayling said.

“His brilliance was put into practice at Bletchley Park during the Second World War where he was pivotal to breaking the Enigma code, helping to end the war and save thousands of lives.

“His later life was overshadowed by his conviction for homosexual activity, a sentence we would now consider unjust and discriminatory and which has now been repealed.

“Dr Turing deserves to be remembered and recognised for his fantastic contribution to the war effort and his legacy to science. A pardon from the Queen is a fitting tribute to an exceptional man.”

Dr Turing died of cyanide poisoning and an inquest recorded a verdict of suicide, although his mother and others maintained his death was accidental.

There has been a long campaign to clear the mathematician’s name, including a well-supported e- petition and private member’s bill, along
with support from leading scientists such as Sir Stephen Hawking.

The pardon under the Royal Prerogative of Mercy will come into effect today. The Justice Secretary has the power to ask the Queen to grant a pardon under the Royal Prerogative of Mercy, for civilians convicted in England and Wales.

A pardon is only normally granted when the person is innocent of the offence and where a request has been made by someone with a vested interest such as a family member. But on this occasion a pardon has been issued without either requirement being met.

In September 2009, then-prime minister Gordon Brown apologised to Dr Turing for prosecuting him as a homosexual after a petition calling for such a move.

An e-petiton – titled “Grant a pardon to Alan Turing” – received 37,404 signatures when it closed in November last year. The request was declined by Lord McNally on the grounds that Dr Turing was properly convicted of what at the time was a criminal offence.

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This is a historic event, coming just before the 60th anniversary of Alan Turing’s passing in Manchester on June 7th, 1954. The historic injustice can never be undone, but it is wonderful that the Government has officially restored Turing’s reputation, and removed the distraction from his amazing scientific and personal achievements.

There are still thousands of others whose lives were changed forever by the law ‘as it was at the time’. No doubt, having shown that we can be generous and do what is necessary regarding Turing, the situation of others will get more consideration.

All thanks must go to the host of wonderful people who have prepared the ground over the years – one hesitates to mention any names, because there were so many, including subscribers to this list.

But, … many thanks to Andrew Hodges for his truly marvellous biography of Turing – there have been others, with their own special qualities (such as being shorter!), but Andrew’s is one of the all-time great biographies, and has done much to help us understand both man and his thinking.

Both UK Government petitions raised the issue of the conviction. The first, initiated by John Graham-Cummings, leading to the Gordon Brown ‘apology’, was a break-through in our thinking, and brought over 30,000 people into the campaign.

The William Jones petition mentioned by Chris Grayling showed you could do it twice! and get even more signatures, building on John’s initiative and the excitement and world-wide reach of the 2012 centenary celebrations.

And then Lord Sharkey, with his private members bill, and John Leech MP carrying the bill forward to the Commons – and a whole spectrum of MPs from different parties, and other famous figures lending their support. And finally, Chris Grayling cutting through the formalities with such decisive effect, and with such nice timing.

On the broader front there was a coming together of many different communities. The gay community, mathematicians, computer scientists and scientists from many areas, artists, musicians, creative thinkers and artists of all kinds, many for very personal reasons, some on the autistic spectrum empowered by the iconic example of Turing’s history.

And the international dimension has been fantastic, moving, exciting, generous, and totally engrossing in its variety and interest. And our
friends in the media have been great too … the list is a long one.

Of course, the list of subscribers receiving these occasional updates contains many people active around Turing-related matters, or just interested in Turing and his ideas, and spreading news and understanding amongst their friends, contacts, or maybe students. Many thanks to you all!

More to follow soon, including a review of media coverage. And a more comprehensive update before the new year.

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ALAN TURING YEARS                          http://www.turingcentenary.eu

## On strong measure zero sets

December 6, 2013

I meant to write a longer blog entry on strong measure zero sets (on the real line $\mathbb R$), but it is getting too long, so it may take me more than I expected. For now, let me record here an argument showing the following:

Theorem. If $X$ is a strong measure zero set and $F$ is a closed measure zero set, then $X+F$ has measure zero.

The argument is similar to the one in

Janusz Pawlikowski. A characterization of strong measure zero sets, Israel J. Math., 93 (1), (1996), 171-183. MR1380640 (97f:28003),

where the result is shown for strong measure zero subsets of $\{0,1\}^{\mathbb N}$. This is actually the easy direction of Pawlikowski’s result, showing that this condition actually characterizes strong measure zero sets, that is, if $X+F$ is measure zero for all closed measure zero sets $F$, then $X$ is strong measure zero. (Since this was intended for my analysis course, and I do not see how to prove Pawlikowski’s argument without some appeal to results in measure theory, I am only including here the easy direction.) Pawlikowski’s argument actually generalizes an earlier key result of Galvin, Mycielski, and Solovay, who proved that a set $X$ has strong measure zero iff it can be made disjoint from any given meager set by translation, that is, iff for any $G$ meager there is a real $r$ with $X+r$ disjoint from $G$.

I proceed with the (short) proof after the fold.